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## Double Jeopardy

It is obvious that 2 + 2 = 2 x 2. But, it there a number you can both add to 3 and multiply by 3 to get the same result?

Try some guesses before you try to work it out.

Now, what happens if the same question is repeated except using one of the numbers 4, 5, 6, ... in place of the 3?
What pattern seems to be developing? What if you used the number n?

Final question: The special case for the number 2 is that its "pair" is itself (i.e. 2 + 2 = 2 x 2). Is 2 the only number with this property? Be careful, someone lost more than \$3000 on this question during "Final Jeopardy" on the television show Jeopardy.

Hint: What is a good problem solving strategy here?
Guess and Check?
Don't get locked into implications of the word "number."

Solution Commentary: For the case of 3:
3 + X = 3X
3 = 2X
X = 3/2

Now, continuing with some algebra, what happens with the numbers 4, 5, 6...n?

What about that last question? Can you solve it using the pattern that was developed? Can you solve it using algebra and the equation n + n = n x n? Or, can you just stop and think....